We were reminded of an explosive political fact this week: The investigations of President Trump’s activities won’t end when special counsel Robert S. Mueller III presents his report to the Justice Department. They’ll move into a new and potentially more divisive phase.

“The congressional investigative effort will be ongoing. It will continue through 2020, and beyond if Trump wins reelection and the Democrats retain the House,” predicted Ty Cobb, a former White House lawyer under Trump, during an interview Thursday. “The Mueller report isn’t going to end everything.”

The prospect for continuing, and perhaps escalating, legal confrontation was clear from the jaw-dropping congressional testimony Wednesday by Michael Cohen, Trump’s former fixer. Cohen said he is cooperating with a probe by the U.S. attorney in Manhattan into other potential criminal issues involving Trump, beyond Mueller’s inquiry. It is impossible to know the seriousness of those probes, or the jeopardy they pose for Trump and his family, but they aren’t going away soon.

Cohen, with his raspy voice and baggy-eyed face, spoke like a penitent mobster as he offered new evidence about what he alleged was Trump’s role in both directing hush-money payments to an adult-film star and massaging financial documents to gain more loans from Deutsche Bank. Cohen also claimed to have “understood the code” on what he asserted was Trump’s record as a “con man” and “cheat.” Congressional committees are already drawing up witness lists to pursue those threads.

Even without Cohen’s headline-grabbing allegations, it became clear this month that House Intelligence Committee Chairman Adam B. Schiff (D-Calif.) and other congressional investigators were crossing Trump’s declared “red line” and beginning to investigate his personal and family finances, including his relationship with Deutsche Bank, perhaps his biggest lender. A Deutsche Bank spokesman told me two weeks ago that the company was cooperating with the investigations.

Democrats will face a growing dilemma about how aggressively they should pursue Trump. House Speaker Nancy Pelosi (D-Calif.) and other leaders have seemed wary about moving quickly toward impeachment, sensing that the public doesn’t want the intense polarization that would accompany an effort to remove the president from office before 2021. But with Cohen’s new allegations of criminal behavior, and an imminent report from Mueller, more Democrats may consider the impeachment option.

As November 2020 approaches, the argument will increase that the issue should be left to the public.

The legal and political battlefields will be shaped by Mueller’s report, and how much of it is made public by Attorney General William P. Barr. Lawyers who have followed the Mueller investigation closely say they doubt the special counsel will present evidence of collusion between the Trump campaign and Russia beyond what he has already revealed in a string of indictments.

Mueller’s findings about Trump’s possible obstruction of justice are more difficult to predict. But even if he has evidence of obstruction, Mueller appears to favor a political adjudication, through the constitutional process of impeachment, rather than a legal one through indictment and trial.

As the Democrat-controlled House moves deeper into legal combat with Trump, it seems increasingly likely that it will bring an epic Supreme Court decision on Congress’s ability to subpoena the Mueller report or, later, Trump administration officials who could testify about the president’s activities. But this legal test will be difficult for Democrats, and not just because the Supreme Court has a conservative majority.

House Democrats might have difficulty winning a case demanding that Barr release all of Mueller’s report. That’s because Congress during the late 1990s, frustrated by seemingly endless investigations by independent counsels, replaced that system with Justice Department regulations that are fairly narrow: A special counsel must provide the attorney general with a “confidential report” about who was or wasn’t indicted, but public release must meet tight Justice Department “guidelines” for disclosing information on criminal investigations.

When Mueller was appointed special counsel in May 2017, some hoped his investigation would bring a decisive resolution, one way or another, perhaps yielding a national sigh of relief akin to President Gerald Ford’s declaration after the Watergate scandal that “our long national nightmare is over.” But Ford’s accession, after the resignation of President Richard M. Nixon, was the result of a bipartisan consultative process, in which conservative Republicans such as Sen. Barry Goldwater (Ariz.) played a key role.

If the fracas surrounding Cohen’s testimony this week proved anything, it’s that there is nothing remotely like bipartisan consensus about how to deal with the allegations about Trump. Instead, this is a political war, and it’s probably heading into a more combative phase, just at the moment some expected it would be ending.